LMFDB - Embedded newform 8002.2.a.d.1.62

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.62
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.18868 q^{3} +1.00000 q^{4} -3.75457 q^{5} +2.18868 q^{6} +3.80095 q^{7} +1.00000 q^{8} +1.79034 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.18868 q^{3} +1.00000 q^{4} -3.75457 q^{5} +2.18868 q^{6} +3.80095 q^{7} +1.00000 q^{8} +1.79034 q^{9} -3.75457 q^{10} -4.46575 q^{11} +2.18868 q^{12} -0.199888 q^{13} +3.80095 q^{14} -8.21758 q^{15} +1.00000 q^{16} +3.79785 q^{17} +1.79034 q^{18} -4.04365 q^{19} -3.75457 q^{20} +8.31907 q^{21} -4.46575 q^{22} -5.66339 q^{23} +2.18868 q^{24} +9.09682 q^{25} -0.199888 q^{26} -2.64757 q^{27} +3.80095 q^{28} -7.75350 q^{29} -8.21758 q^{30} -4.02684 q^{31} +1.00000 q^{32} -9.77411 q^{33} +3.79785 q^{34} -14.2709 q^{35} +1.79034 q^{36} +5.28226 q^{37} -4.04365 q^{38} -0.437493 q^{39} -3.75457 q^{40} +1.82035 q^{41} +8.31907 q^{42} -3.70994 q^{43} -4.46575 q^{44} -6.72196 q^{45} -5.66339 q^{46} -0.558405 q^{47} +2.18868 q^{48} +7.44719 q^{49} +9.09682 q^{50} +8.31230 q^{51} -0.199888 q^{52} -6.21854 q^{53} -2.64757 q^{54} +16.7670 q^{55} +3.80095 q^{56} -8.85028 q^{57} -7.75350 q^{58} -6.28765 q^{59} -8.21758 q^{60} +5.79993 q^{61} -4.02684 q^{62} +6.80498 q^{63} +1.00000 q^{64} +0.750496 q^{65} -9.77411 q^{66} -3.91376 q^{67} +3.79785 q^{68} -12.3954 q^{69} -14.2709 q^{70} -6.78965 q^{71} +1.79034 q^{72} -1.97552 q^{73} +5.28226 q^{74} +19.9101 q^{75} -4.04365 q^{76} -16.9741 q^{77} -0.437493 q^{78} -1.26418 q^{79} -3.75457 q^{80} -11.1657 q^{81} +1.82035 q^{82} +2.06681 q^{83} +8.31907 q^{84} -14.2593 q^{85} -3.70994 q^{86} -16.9700 q^{87} -4.46575 q^{88} -0.00450249 q^{89} -6.72196 q^{90} -0.759765 q^{91} -5.66339 q^{92} -8.81347 q^{93} -0.558405 q^{94} +15.1822 q^{95} +2.18868 q^{96} +8.19392 q^{97} +7.44719 q^{98} -7.99520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.18868	1.26364	0.631819	−	0.775116i	$-0.282309\pi$
$3$	2.18868	1.26364	0.631819	+	0.775116i	$0.282309\pi$
$4$	1.00000	0.500000
$5$	−3.75457	−1.67910	−0.839548	−	0.543285i	$-0.817180\pi$
$5$	−3.75457	−1.67910	−0.839548	+	0.543285i	$0.817180\pi$
$6$	2.18868	0.893527
$7$	3.80095	1.43662	0.718311	−	0.695722i	$-0.244915\pi$
$7$	3.80095	1.43662	0.718311	+	0.695722i	$0.244915\pi$
$8$	1.00000	0.353553
$9$	1.79034	0.596779
$10$	−3.75457	−1.18730
$11$	−4.46575	−1.34647	−0.673237	−	0.739427i	$-0.735097\pi$
$11$	−4.46575	−1.34647	−0.673237	+	0.739427i	$0.735097\pi$
$12$	2.18868	0.631819
$13$	−0.199888	−0.0554391	−0.0277195	−	0.999616i	$-0.508825\pi$
$13$	−0.199888	−0.0554391	−0.0277195	+	0.999616i	$0.508825\pi$
$14$	3.80095	1.01585
$15$	−8.21758	−2.12177
$16$	1.00000	0.250000
$17$	3.79785	0.921115	0.460557	−	0.887630i	$-0.347650\pi$
$17$	3.79785	0.921115	0.460557	+	0.887630i	$0.347650\pi$
$18$	1.79034	0.421987
$19$	−4.04365	−0.927678	−0.463839	−	0.885920i	$-0.653528\pi$
$19$	−4.04365	−0.927678	−0.463839	+	0.885920i	$0.653528\pi$
$20$	−3.75457	−0.839548
$21$	8.31907	1.81537
$22$	−4.46575	−0.952101
$23$	−5.66339	−1.18090	−0.590450	−	0.807075i	$-0.701050\pi$
$23$	−5.66339	−1.18090	−0.590450	+	0.807075i	$0.701050\pi$
$24$	2.18868	0.446763
$25$	9.09682	1.81936
$26$	−0.199888	−0.0392013
$27$	−2.64757	−0.509525
$28$	3.80095	0.718311
$29$	−7.75350	−1.43979	−0.719894	−	0.694084i	$-0.755810\pi$
$29$	−7.75350	−1.43979	−0.719894	+	0.694084i	$0.755810\pi$
$30$	−8.21758	−1.50032
$31$	−4.02684	−0.723241	−0.361621	−	0.932325i	$-0.617776\pi$
$31$	−4.02684	−0.723241	−0.361621	+	0.932325i	$0.617776\pi$
$32$	1.00000	0.176777
$33$	−9.77411	−1.70145
$34$	3.79785	0.651326
$35$	−14.2709	−2.41223
$36$	1.79034	0.298390
$37$	5.28226	0.868399	0.434199	−	0.900817i	$-0.357031\pi$
$37$	5.28226	0.868399	0.434199	+	0.900817i	$0.357031\pi$
$38$	−4.04365	−0.655967
$39$	−0.437493	−0.0700549
$40$	−3.75457	−0.593650
$41$	1.82035	0.284290	0.142145	−	0.989846i	$-0.454600\pi$
$41$	1.82035	0.284290	0.142145	+	0.989846i	$0.454600\pi$
$42$	8.31907	1.28366
$43$	−3.70994	−0.565761	−0.282880	−	0.959155i	$-0.591290\pi$
$43$	−3.70994	−0.565761	−0.282880	+	0.959155i	$0.591290\pi$
$44$	−4.46575	−0.673237
$45$	−6.72196	−1.00205
$46$	−5.66339	−0.835022
$47$	−0.558405	−0.0814518	−0.0407259	−	0.999170i	$-0.512967\pi$
$47$	−0.558405	−0.0814518	−0.0407259	+	0.999170i	$0.512967\pi$
$48$	2.18868	0.315909
$49$	7.44719	1.06388
$50$	9.09682	1.28649
$51$	8.31230	1.16396
$52$	−0.199888	−0.0277195
$53$	−6.21854	−0.854182	−0.427091	−	0.904209i	$-0.640462\pi$
$53$	−6.21854	−0.854182	−0.427091	+	0.904209i	$0.640462\pi$
$54$	−2.64757	−0.360288
$55$	16.7670	2.26086
$56$	3.80095	0.507923
$57$	−8.85028	−1.17225
$58$	−7.75350	−1.01808
$59$	−6.28765	−0.818583	−0.409291	−	0.912404i	$-0.634224\pi$
$59$	−6.28765	−0.818583	−0.409291	+	0.912404i	$0.634224\pi$
$60$	−8.21758	−1.06088
$61$	5.79993	0.742605	0.371302	−	0.928512i	$-0.378911\pi$
$61$	5.79993	0.742605	0.371302	+	0.928512i	$0.378911\pi$
$62$	−4.02684	−0.511409
$63$	6.80498	0.857347
$64$	1.00000	0.125000
$65$	0.750496	0.0930876
$66$	−9.77411	−1.20311
$67$	−3.91376	−0.478142	−0.239071	−	0.971002i	$-0.576843\pi$
$67$	−3.91376	−0.478142	−0.239071	+	0.971002i	$0.576843\pi$
$68$	3.79785	0.460557
$69$	−12.3954	−1.49223
$70$	−14.2709	−1.70570
$71$	−6.78965	−0.805783	−0.402892	−	0.915248i	$-0.631995\pi$
$71$	−6.78965	−0.805783	−0.402892	+	0.915248i	$0.631995\pi$
$72$	1.79034	0.210993
$73$	−1.97552	−0.231217	−0.115609	−	0.993295i	$-0.536882\pi$
$73$	−1.97552	−0.231217	−0.115609	+	0.993295i	$0.536882\pi$
$74$	5.28226	0.614051
$75$	19.9101	2.29902
$76$	−4.04365	−0.463839
$77$	−16.9741	−1.93437
$78$	−0.437493	−0.0495363
$79$	−1.26418	−0.142231	−0.0711155	−	0.997468i	$-0.522656\pi$
$79$	−1.26418	−0.142231	−0.0711155	+	0.997468i	$0.522656\pi$
$80$	−3.75457	−0.419774
$81$	−11.1657	−1.24063
$82$	1.82035	0.201024
$83$	2.06681	0.226862	0.113431	−	0.993546i	$-0.463816\pi$
$83$	2.06681	0.226862	0.113431	+	0.993546i	$0.463816\pi$
$84$	8.31907	0.907685
$85$	−14.2593	−1.54664
$86$	−3.70994	−0.400053
$87$	−16.9700	−1.81937
$88$	−4.46575	−0.476050
$89$	−0.00450249	−0.000477263 0	−0.000238632	−	1.00000i	$-0.500076\pi$
$89$	−0.00450249	−0.000477263 0	−0.000238632		1.00000i	$0.500076\pi$
$90$	−6.72196	−0.708557
$91$	−0.759765	−0.0796450
$92$	−5.66339	−0.590450
$93$	−8.81347	−0.913915
$94$	−0.558405	−0.0575951
$95$	15.1822	1.55766
$96$	2.18868	0.223382
$97$	8.19392	0.831967	0.415983	−	0.909372i	$-0.363437\pi$
$97$	8.19392	0.831967	0.415983	+	0.909372i	$0.363437\pi$
$98$	7.44719	0.752279
$99$	−7.99520	−0.803548
$100$	9.09682	0.909682
$101$	−2.60582	−0.259289	−0.129644	−	0.991561i	$-0.541384\pi$
$101$	−2.60582	−0.259289	−0.129644	+	0.991561i	$0.541384\pi$
$102$	8.31230	0.823041
$103$	6.34603	0.625293	0.312646	−	0.949870i	$-0.398785\pi$
$103$	6.34603	0.625293	0.312646	+	0.949870i	$0.398785\pi$
$104$	−0.199888	−0.0196007
$105$	−31.2346	−3.04818
$106$	−6.21854	−0.603998
$107$	−9.58654	−0.926765	−0.463383	−	0.886158i	$-0.653364\pi$
$107$	−9.58654	−0.926765	−0.463383	+	0.886158i	$0.653364\pi$
$108$	−2.64757	−0.254762
$109$	−2.62018	−0.250968	−0.125484	−	0.992096i	$-0.540048\pi$
$109$	−2.62018	−0.250968	−0.125484	+	0.992096i	$0.540048\pi$
$110$	16.7670	1.59867
$111$	11.5612	1.09734
$112$	3.80095	0.359156
$113$	−13.5224	−1.27208	−0.636041	−	0.771655i	$-0.719429\pi$
$113$	−13.5224	−1.27208	−0.636041	+	0.771655i	$0.719429\pi$
$114$	−8.85028	−0.828905
$115$	21.2636	1.98284
$116$	−7.75350	−0.719894
$117$	−0.357868	−0.0330849
$118$	−6.28765	−0.578825
$119$	14.4354	1.32329
$120$	−8.21758	−0.750159
$121$	8.94291	0.812992
$122$	5.79993	0.525101
$123$	3.98417	0.359240
$124$	−4.02684	−0.361621
$125$	−15.3818	−1.37579
$126$	6.80498	0.606236
$127$	15.2598	1.35409	0.677044	−	0.735942i	$-0.263261\pi$
$127$	15.2598	1.35409	0.677044	+	0.735942i	$0.263261\pi$
$128$	1.00000	0.0883883
$129$	−8.11989	−0.714917
$130$	0.750496	0.0658228
$131$	−10.0554	−0.878544	−0.439272	−	0.898354i	$-0.644764\pi$
$131$	−10.0554	−0.878544	−0.439272	+	0.898354i	$0.644764\pi$
$132$	−9.77411	−0.850727
$133$	−15.3697	−1.33272
$134$	−3.91376	−0.338098
$135$	9.94049	0.855541
$136$	3.79785	0.325663
$137$	−1.40835	−0.120323	−0.0601616	−	0.998189i	$-0.519162\pi$
$137$	−1.40835	−0.120323	−0.0601616	+	0.998189i	$0.519162\pi$
$138$	−12.3954	−1.05516
$139$	13.0209	1.10442	0.552211	−	0.833704i	$-0.313784\pi$
$139$	13.0209	1.10442	0.552211	+	0.833704i	$0.313784\pi$
$140$	−14.2709	−1.20611
$141$	−1.22217	−0.102926
$142$	−6.78965	−0.569775
$143$	0.892651	0.0746473
$144$	1.79034	0.149195
$145$	29.1111	2.41754
$146$	−1.97552	−0.163495
$147$	16.2995	1.34436
$148$	5.28226	0.434199
$149$	−17.2366	−1.41208	−0.706041	−	0.708171i	$-0.749520\pi$
$149$	−17.2366	−1.41208	−0.706041	+	0.708171i	$0.749520\pi$
$150$	19.9101	1.62565
$151$	−6.84874	−0.557343	−0.278671	−	0.960387i	$-0.589894\pi$
$151$	−6.84874	−0.557343	−0.278671	+	0.960387i	$0.589894\pi$
$152$	−4.04365	−0.327984
$153$	6.79944	0.549702
$154$	−16.9741	−1.36781
$155$	15.1191	1.21439
$156$	−0.437493	−0.0350274
$157$	1.48927	0.118857	0.0594284	−	0.998233i	$-0.481072\pi$
$157$	1.48927	0.118857	0.0594284	+	0.998233i	$0.481072\pi$
$158$	−1.26418	−0.100572
$159$	−13.6104	−1.07938
$160$	−3.75457	−0.296825
$161$	−21.5263	−1.69651
$162$	−11.1657	−0.877261
$163$	−2.76205	−0.216340	−0.108170	−	0.994132i	$-0.534499\pi$
$163$	−2.76205	−0.216340	−0.108170	+	0.994132i	$0.534499\pi$
$164$	1.82035	0.142145
$165$	36.6976	2.85691
$166$	2.06681	0.160416
$167$	12.4856	0.966167	0.483084	−	0.875574i	$-0.339517\pi$
$167$	12.4856	0.966167	0.483084	+	0.875574i	$0.339517\pi$
$168$	8.31907	0.641830
$169$	−12.9600	−0.996927
$170$	−14.2593	−1.09364
$171$	−7.23951	−0.553619
$172$	−3.70994	−0.282880
$173$	19.8687	1.51059	0.755295	−	0.655384i	$-0.227493\pi$
$173$	19.8687	1.51059	0.755295	+	0.655384i	$0.227493\pi$
$174$	−16.9700	−1.28649
$175$	34.5765	2.61374
$176$	−4.46575	−0.336618
$177$	−13.7617	−1.03439
$178$	−0.00450249	−0.000337476 0
$179$	9.27663	0.693368	0.346684	−	0.937982i	$-0.387308\pi$
$179$	9.27663	0.693368	0.346684	+	0.937982i	$0.387308\pi$
$180$	−6.72196	−0.501025
$181$	−7.26517	−0.540016	−0.270008	−	0.962858i	$-0.587026\pi$
$181$	−7.26517	−0.540016	−0.270008	+	0.962858i	$0.587026\pi$
$182$	−0.759765	−0.0563175
$183$	12.6942	0.938383
$184$	−5.66339	−0.417511
$185$	−19.8326	−1.45813
$186$	−8.81347	−0.646235
$187$	−16.9603	−1.24026
$188$	−0.558405	−0.0407259
$189$	−10.0633	−0.731994
$190$	15.1822	1.10143
$191$	13.6492	0.987620	0.493810	−	0.869570i	$-0.335604\pi$
$191$	13.6492	0.987620	0.493810	+	0.869570i	$0.335604\pi$
$192$	2.18868	0.157955
$193$	−17.0902	−1.23018	−0.615090	−	0.788457i	$-0.710880\pi$
$193$	−17.0902	−1.23018	−0.615090	+	0.788457i	$0.710880\pi$
$194$	8.19392	0.588289
$195$	1.64260	0.117629
$196$	7.44719	0.531942
$197$	−11.5161	−0.820490	−0.410245	−	0.911975i	$-0.634557\pi$
$197$	−11.5161	−0.820490	−0.410245	+	0.911975i	$0.634557\pi$
$198$	−7.99520	−0.568194
$199$	2.43370	0.172520	0.0862602	−	0.996273i	$-0.472508\pi$
$199$	2.43370	0.172520	0.0862602	+	0.996273i	$0.472508\pi$
$200$	9.09682	0.643243
$201$	−8.56599	−0.604199
$202$	−2.60582	−0.183345
$203$	−29.4706	−2.06843
$204$	8.31230	0.581978
$205$	−6.83463	−0.477351
$206$	6.34603	0.442149
$207$	−10.1394	−0.704736
$208$	−0.199888	−0.0138598
$209$	18.0579	1.24909
$210$	−31.2346	−2.15539
$211$	−4.22990	−0.291198	−0.145599	−	0.989344i	$-0.546511\pi$
$211$	−4.22990	−0.291198	−0.145599	+	0.989344i	$0.546511\pi$
$212$	−6.21854	−0.427091
$213$	−14.8604	−1.01822
$214$	−9.58654	−0.655322
$215$	13.9293	0.949967
$216$	−2.64757	−0.180144
$217$	−15.3058	−1.03902
$218$	−2.62018	−0.177461
$219$	−4.32379	−0.292175
$220$	16.7670	1.13043
$221$	−0.759147	−0.0510658
$222$	11.5612	0.775937
$223$	−23.1991	−1.55353	−0.776765	−	0.629791i	$-0.783141\pi$
$223$	−23.1991	−1.55353	−0.776765	+	0.629791i	$0.783141\pi$
$224$	3.80095	0.253961
$225$	16.2864	1.08576
$226$	−13.5224	−0.899497
$227$	−12.8919	−0.855668	−0.427834	−	0.903857i	$-0.640723\pi$
$227$	−12.8919	−0.855668	−0.427834	+	0.903857i	$0.640723\pi$
$228$	−8.85028	−0.586124
$229$	2.02753	0.133983	0.0669915	−	0.997754i	$-0.478660\pi$
$229$	2.02753	0.133983	0.0669915	+	0.997754i	$0.478660\pi$
$230$	21.2636	1.40208
$231$	−37.1509	−2.44435
$232$	−7.75350	−0.509042
$233$	1.82425	0.119511	0.0597553	−	0.998213i	$-0.480968\pi$
$233$	1.82425	0.119511	0.0597553	+	0.998213i	$0.480968\pi$
$234$	−0.357868	−0.0233946
$235$	2.09657	0.136765
$236$	−6.28765	−0.409291
$237$	−2.76688	−0.179728
$238$	14.4354	0.935710
$239$	4.36329	0.282238	0.141119	−	0.989993i	$-0.454930\pi$
$239$	4.36329	0.282238	0.141119	+	0.989993i	$0.454930\pi$
$240$	−8.21758	−0.530442
$241$	−2.16050	−0.139170	−0.0695850	−	0.997576i	$-0.522168\pi$
$241$	−2.16050	−0.139170	−0.0695850	+	0.997576i	$0.522168\pi$
$242$	8.94291	0.574872
$243$	−16.4955	−1.05819
$244$	5.79993	0.371302
$245$	−27.9610	−1.78636
$246$	3.98417	0.254021
$247$	0.808280	0.0514296
$248$	−4.02684	−0.255704
$249$	4.52359	0.286671
$250$	−15.3818	−0.972832
$251$	−11.8144	−0.745720	−0.372860	−	0.927888i	$-0.621623\pi$
$251$	−11.8144	−0.745720	−0.372860	+	0.927888i	$0.621623\pi$
$252$	6.80498	0.428673
$253$	25.2913	1.59005
$254$	15.2598	0.957485
$255$	−31.2091	−1.95439
$256$	1.00000	0.0625000
$257$	23.6939	1.47798	0.738991	−	0.673715i	$-0.235303\pi$
$257$	23.6939	1.47798	0.738991	+	0.673715i	$0.235303\pi$
$258$	−8.11989	−0.505522
$259$	20.0776	1.24756
$260$	0.750496	0.0465438
$261$	−13.8814	−0.859236
$262$	−10.0554	−0.621225
$263$	−31.8871	−1.96624	−0.983122	−	0.182950i	$-0.941435\pi$
$263$	−31.8871	−1.96624	−0.983122	+	0.182950i	$0.941435\pi$
$264$	−9.77411	−0.601555
$265$	23.3480	1.43425
$266$	−15.3697	−0.942377
$267$	−0.00985453	−0.000603088 0
$268$	−3.91376	−0.239071
$269$	−15.8072	−0.963780	−0.481890	−	0.876232i	$-0.660050\pi$
$269$	−15.8072	−0.963780	−0.481890	+	0.876232i	$0.660050\pi$
$270$	9.94049	0.604959
$271$	30.6895	1.86425	0.932127	−	0.362131i	$-0.117951\pi$
$271$	30.6895	1.86425	0.932127	+	0.362131i	$0.117951\pi$
$272$	3.79785	0.230279
$273$	−1.66289	−0.100642
$274$	−1.40835	−0.0850814
$275$	−40.6241	−2.44973
$276$	−12.3954	−0.746114
$277$	8.48866	0.510034	0.255017	−	0.966937i	$-0.417919\pi$
$277$	8.48866	0.510034	0.255017	+	0.966937i	$0.417919\pi$
$278$	13.0209	0.780945
$279$	−7.20940	−0.431616
$280$	−14.2709	−0.852851
$281$	27.3541	1.63181	0.815905	−	0.578186i	$-0.196239\pi$
$281$	27.3541	1.63181	0.815905	+	0.578186i	$0.196239\pi$
$282$	−1.22217	−0.0727793
$283$	5.61152	0.333570	0.166785	−	0.985993i	$-0.446661\pi$
$283$	5.61152	0.333570	0.166785	+	0.985993i	$0.446661\pi$
$284$	−6.78965	−0.402892
$285$	33.2290	1.96832
$286$	0.892651	0.0527836
$287$	6.91904	0.408418
$288$	1.79034	0.105497
$289$	−2.57631	−0.151548
$290$	29.1111	1.70946
$291$	17.9339	1.05130
$292$	−1.97552	−0.115609
$293$	−12.7314	−0.743775	−0.371887	−	0.928278i	$-0.621289\pi$
$293$	−12.7314	−0.743775	−0.371887	+	0.928278i	$0.621289\pi$
$294$	16.2995	0.950608
$295$	23.6075	1.37448
$296$	5.28226	0.307025
$297$	11.8234	0.686061
$298$	−17.2366	−0.998492
$299$	1.13205	0.0654680
$300$	19.9101	1.14951
$301$	−14.1013	−0.812785
$302$	−6.84874	−0.394101
$303$	−5.70331	−0.327647
$304$	−4.04365	−0.231919
$305$	−21.7763	−1.24690
$306$	6.79944	0.388698
$307$	20.4276	1.16586	0.582931	−	0.812521i	$-0.301906\pi$
$307$	20.4276	1.16586	0.582931	+	0.812521i	$0.301906\pi$
$308$	−16.9741	−0.967187
$309$	13.8894	0.790143
$310$	15.1191	0.858705
$311$	19.2019	1.08884	0.544420	−	0.838813i	$-0.316750\pi$
$311$	19.2019	1.08884	0.544420	+	0.838813i	$0.316750\pi$
$312$	−0.437493	−0.0247681
$313$	−9.44571	−0.533903	−0.266952	−	0.963710i	$-0.586016\pi$
$313$	−9.44571	−0.533903	−0.266952	+	0.963710i	$0.586016\pi$
$314$	1.48927	0.0840445
$315$	−25.5498	−1.43957
$316$	−1.26418	−0.0711155
$317$	21.8744	1.22859	0.614295	−	0.789077i	$-0.289441\pi$
$317$	21.8744	1.22859	0.614295	+	0.789077i	$0.289441\pi$
$318$	−13.6104	−0.763234
$319$	34.6252	1.93864
$320$	−3.75457	−0.209887
$321$	−20.9819	−1.17110
$322$	−21.5263	−1.19961
$323$	−15.3572	−0.854498
$324$	−11.1657	−0.620317
$325$	−1.81835	−0.100864
$326$	−2.76205	−0.152976
$327$	−5.73474	−0.317132
$328$	1.82035	0.100512
$329$	−2.12247	−0.117015
$330$	36.6976	2.02014
$331$	1.22429	0.0672932	0.0336466	−	0.999434i	$-0.489288\pi$
$331$	1.22429	0.0672932	0.0336466	+	0.999434i	$0.489288\pi$
$332$	2.06681	0.113431
$333$	9.45704	0.518243
$334$	12.4856	0.683183
$335$	14.6945	0.802847
$336$	8.31907	0.453842
$337$	−4.05219	−0.220737	−0.110368	−	0.993891i	$-0.535203\pi$
$337$	−4.05219	−0.220737	−0.110368	+	0.993891i	$0.535203\pi$
$338$	−12.9600	−0.704933
$339$	−29.5963	−1.60745
$340$	−14.2593	−0.773320
$341$	17.9828	0.973825
$342$	−7.23951	−0.391468
$343$	1.69973	0.0917767
$344$	−3.70994	−0.200027
$345$	46.5394	2.50560
$346$	19.8687	1.06815
$347$	16.0307	0.860573	0.430286	−	0.902692i	$-0.358413\pi$
$347$	16.0307	0.860573	0.430286	+	0.902692i	$0.358413\pi$
$348$	−16.9700	−0.909685
$349$	−1.01321	−0.0542361	−0.0271181	−	0.999632i	$-0.508633\pi$
$349$	−1.01321	−0.0542361	−0.0271181	+	0.999632i	$0.508633\pi$
$350$	34.5765	1.84819
$351$	0.529218	0.0282476
$352$	−4.46575	−0.238025
$353$	−24.0513	−1.28012	−0.640061	−	0.768324i	$-0.721091\pi$
$353$	−24.0513	−1.28012	−0.640061	+	0.768324i	$0.721091\pi$
$354$	−13.7617	−0.731425
$355$	25.4922	1.35299
$356$	−0.00450249	−0.000238632 0
$357$	31.5946	1.67216
$358$	9.27663	0.490285
$359$	3.89641	0.205645	0.102822	−	0.994700i	$-0.467213\pi$
$359$	3.89641	0.205645	0.102822	+	0.994700i	$0.467213\pi$
$360$	−6.72196	−0.354278
$361$	−2.64886	−0.139414
$362$	−7.26517	−0.381849
$363$	19.5732	1.02733
$364$	−0.759765	−0.0398225
$365$	7.41724	0.388236
$366$	12.6942	0.663537
$367$	21.3265	1.11324	0.556618	−	0.830768i	$-0.312099\pi$
$367$	21.3265	1.11324	0.556618	+	0.830768i	$0.312099\pi$
$368$	−5.66339	−0.295225
$369$	3.25904	0.169659
$370$	−19.8326	−1.03105
$371$	−23.6363	−1.22714
$372$	−8.81347	−0.456957
$373$	−16.7562	−0.867601	−0.433801	−	0.901009i	$-0.642828\pi$
$373$	−16.7562	−0.867601	−0.433801	+	0.901009i	$0.642828\pi$
$374$	−16.9603	−0.876994
$375$	−33.6660	−1.73850
$376$	−0.558405	−0.0287976
$377$	1.54983	0.0798205
$378$	−10.0633	−0.517598
$379$	−25.3660	−1.30296	−0.651482	−	0.758664i	$-0.725852\pi$
$379$	−25.3660	−1.30296	−0.651482	+	0.758664i	$0.725852\pi$
$380$	15.1822	0.778830
$381$	33.3989	1.71108
$382$	13.6492	0.698353
$383$	23.3647	1.19388	0.596941	−	0.802285i	$-0.296383\pi$
$383$	23.3647	1.19388	0.596941	+	0.802285i	$0.296383\pi$
$384$	2.18868	0.111691
$385$	63.7304	3.24800
$386$	−17.0902	−0.869868
$387$	−6.64205	−0.337635
$388$	8.19392	0.415983
$389$	0.275532	0.0139700	0.00698501	−	0.999976i	$-0.497777\pi$
$389$	0.275532	0.0139700	0.00698501	+	0.999976i	$0.497777\pi$
$390$	1.64260	0.0831762
$391$	−21.5087	−1.08774
$392$	7.44719	0.376140
$393$	−22.0081	−1.11016
$394$	−11.5161	−0.580174
$395$	4.74644	0.238819
$396$	−7.99520	−0.401774
$397$	−20.3216	−1.01991	−0.509957	−	0.860200i	$-0.670339\pi$
$397$	−20.3216	−1.01991	−0.509957	+	0.860200i	$0.670339\pi$
$398$	2.43370	0.121990
$399$	−33.6394	−1.68408
$400$	9.09682	0.454841
$401$	27.2939	1.36299	0.681496	−	0.731821i	$-0.261329\pi$
$401$	27.2939	1.36299	0.681496	+	0.731821i	$0.261329\pi$
$402$	−8.56599	−0.427233
$403$	0.804918	0.0400958
$404$	−2.60582	−0.129644
$405$	41.9225	2.08314
$406$	−29.4706	−1.46260
$407$	−23.5893	−1.16928
$408$	8.31230	0.411520
$409$	−34.2077	−1.69146	−0.845731	−	0.533609i	$-0.820835\pi$
$409$	−34.2077	−1.69146	−0.845731	+	0.533609i	$0.820835\pi$
$410$	−6.83463	−0.337538
$411$	−3.08243	−0.152045
$412$	6.34603	0.312646
$413$	−23.8990	−1.17599
$414$	−10.1394	−0.498324
$415$	−7.75999	−0.380923
$416$	−0.199888	−0.00980034
$417$	28.4987	1.39559
$418$	18.0579	0.883243
$419$	−24.3918	−1.19162	−0.595809	−	0.803126i	$-0.703169\pi$
$419$	−24.3918	−1.19162	−0.595809	+	0.803126i	$0.703169\pi$
$420$	−31.2346	−1.52409
$421$	16.2589	0.792409	0.396205	−	0.918162i	$-0.370327\pi$
$421$	16.2589	0.792409	0.396205	+	0.918162i	$0.370327\pi$
$422$	−4.22990	−0.205908
$423$	−0.999735	−0.0486088
$424$	−6.21854	−0.301999
$425$	34.5484	1.67584
$426$	−14.8604	−0.719989
$427$	22.0452	1.06684
$428$	−9.58654	−0.463383
$429$	1.95373	0.0943271
$430$	13.9293	0.671728
$431$	17.1386	0.825538	0.412769	−	0.910836i	$-0.364562\pi$
$431$	17.1386	0.825538	0.412769	+	0.910836i	$0.364562\pi$
$432$	−2.64757	−0.127381
$433$	−15.0689	−0.724163	−0.362082	−	0.932146i	$-0.617934\pi$
$433$	−15.0689	−0.724163	−0.362082	+	0.932146i	$0.617934\pi$
$434$	−15.3058	−0.734701
$435$	63.7150	3.05490
$436$	−2.62018	−0.125484
$437$	22.9008	1.09549
$438$	−4.32379	−0.206599
$439$	0.583000	0.0278250	0.0139125	−	0.999903i	$-0.495571\pi$
$439$	0.583000	0.0278250	0.0139125	+	0.999903i	$0.495571\pi$
$440$	16.7670	0.799335
$441$	13.3330	0.634904
$442$	−0.759147	−0.0361089
$443$	11.1295	0.528779	0.264389	−	0.964416i	$-0.414830\pi$
$443$	11.1295	0.528779	0.264389	+	0.964416i	$0.414830\pi$
$444$	11.5612	0.548671
$445$	0.0169049	0.000801371 0
$446$	−23.1991	−1.09851
$447$	−37.7256	−1.78436
$448$	3.80095	0.179578
$449$	20.7888	0.981085	0.490543	−	0.871417i	$-0.336799\pi$
$449$	20.7888	0.981085	0.490543	+	0.871417i	$0.336799\pi$
$450$	16.2864	0.767748
$451$	−8.12921	−0.382790
$452$	−13.5224	−0.636041
$453$	−14.9897	−0.704279
$454$	−12.8919	−0.605049
$455$	2.85259	0.133732
$456$	−8.85028	−0.414452
$457$	−25.0136	−1.17009	−0.585045	−	0.811001i	$-0.698923\pi$
$457$	−25.0136	−1.17009	−0.585045	+	0.811001i	$0.698923\pi$
$458$	2.02753	0.0947403
$459$	−10.0551	−0.469331
$460$	21.2636	0.991422
$461$	13.7411	0.639985	0.319993	−	0.947420i	$-0.396320\pi$
$461$	13.7411	0.639985	0.319993	+	0.947420i	$0.396320\pi$
$462$	−37.1509	−1.72841
$463$	−6.18764	−0.287564	−0.143782	−	0.989609i	$-0.545926\pi$
$463$	−6.18764	−0.287564	−0.143782	+	0.989609i	$0.545926\pi$
$464$	−7.75350	−0.359947
$465$	33.0908	1.53455
$466$	1.82425	0.0845067
$467$	21.2399	0.982866	0.491433	−	0.870915i	$-0.336473\pi$
$467$	21.2399	0.982866	0.491433	+	0.870915i	$0.336473\pi$
$468$	−0.357868	−0.0165425
$469$	−14.8760	−0.686910
$470$	2.09657	0.0967078
$471$	3.25955	0.150192
$472$	−6.28765	−0.289413
$473$	16.5677	0.761782
$474$	−2.76688	−0.127087
$475$	−36.7844	−1.68778
$476$	14.4354	0.661647
$477$	−11.1333	−0.509758
$478$	4.36329	0.199572
$479$	3.40279	0.155477	0.0777387	−	0.996974i	$-0.475230\pi$
$479$	3.40279	0.155477	0.0777387	+	0.996974i	$0.475230\pi$
$480$	−8.21758	−0.375079
$481$	−1.05586	−0.0481432
$482$	−2.16050	−0.0984080
$483$	−47.1142	−2.14377
$484$	8.94291	0.406496
$485$	−30.7647	−1.39695
$486$	−16.4955	−0.748251
$487$	−15.7055	−0.711683	−0.355842	−	0.934546i	$-0.615806\pi$
$487$	−15.7055	−0.711683	−0.355842	+	0.934546i	$0.615806\pi$
$488$	5.79993	0.262550
$489$	−6.04525	−0.273376
$490$	−27.9610	−1.26315
$491$	23.4224	1.05704	0.528520	−	0.848921i	$-0.322747\pi$
$491$	23.4224	1.05704	0.528520	+	0.848921i	$0.322747\pi$
$492$	3.98417	0.179620
$493$	−29.4466	−1.32621
$494$	0.808280	0.0363662
$495$	30.0186	1.34923
$496$	−4.02684	−0.180810
$497$	−25.8071	−1.15761
$498$	4.52359	0.202707
$499$	−33.8288	−1.51439	−0.757194	−	0.653190i	$-0.773430\pi$
$499$	−33.8288	−1.51439	−0.757194	+	0.653190i	$0.773430\pi$
$500$	−15.3818	−0.687896
$501$	27.3271	1.22088
$502$	−11.8144	−0.527304
$503$	4.43823	0.197891	0.0989455	−	0.995093i	$-0.468453\pi$
$503$	4.43823	0.197891	0.0989455	+	0.995093i	$0.468453\pi$
$504$	6.80498	0.303118
$505$	9.78374	0.435371
$506$	25.2913	1.12434
$507$	−28.3654	−1.25975
$508$	15.2598	0.677044
$509$	−32.2225	−1.42824	−0.714118	−	0.700025i	$-0.753172\pi$
$509$	−32.2225	−1.42824	−0.714118	+	0.700025i	$0.753172\pi$
$510$	−31.2091	−1.38196
$511$	−7.50885	−0.332172
$512$	1.00000	0.0441942
$513$	10.7058	0.472675
$514$	23.6939	1.04509
$515$	−23.8266	−1.04993
$516$	−8.11989	−0.357458
$517$	2.49370	0.109673
$518$	20.0776	0.882159
$519$	43.4864	1.90884
$520$	0.750496	0.0329114
$521$	−29.2113	−1.27977	−0.639886	−	0.768470i	$-0.721018\pi$
$521$	−29.2113	−1.27977	−0.639886	+	0.768470i	$0.721018\pi$
$522$	−13.8814	−0.607572
$523$	−30.5478	−1.33576	−0.667882	−	0.744267i	$-0.732799\pi$
$523$	−30.5478	−1.33576	−0.667882	+	0.744267i	$0.732799\pi$
$524$	−10.0554	−0.439272
$525$	75.6771	3.30282
$526$	−31.8871	−1.39034
$527$	−15.2933	−0.666188
$528$	−9.77411	−0.425364
$529$	9.07403	0.394523
$530$	23.3480	1.01417
$531$	−11.2570	−0.488513
$532$	−15.3697	−0.666361
$533$	−0.363866	−0.0157608
$534$	−0.00985453	−0.000426447 0
$535$	35.9934	1.55613
$536$	−3.91376	−0.169049
$537$	20.3036	0.876165
$538$	−15.8072	−0.681496
$539$	−33.2573	−1.43249
$540$	9.94049	0.427770
$541$	−20.6733	−0.888816	−0.444408	−	0.895824i	$-0.646586\pi$
$541$	−20.6733	−0.888816	−0.444408	+	0.895824i	$0.646586\pi$
$542$	30.6895	1.31823
$543$	−15.9012	−0.682385
$544$	3.79785	0.162832
$545$	9.83766	0.421399
$546$	−1.66289	−0.0711649
$547$	27.1684	1.16164	0.580819	−	0.814032i	$-0.302732\pi$
$547$	27.1684	1.16164	0.580819	+	0.814032i	$0.302732\pi$
$548$	−1.40835	−0.0601616
$549$	10.3838	0.443171
$550$	−40.6241	−1.73222
$551$	31.3525	1.33566
$552$	−12.3954	−0.527582
$553$	−4.80507	−0.204332
$554$	8.48866	0.360649
$555$	−43.4074	−1.84254
$556$	13.0209	0.552211
$557$	16.7030	0.707731	0.353865	−	0.935296i	$-0.384867\pi$
$557$	16.7030	0.707731	0.353865	+	0.935296i	$0.384867\pi$
$558$	−7.20940	−0.305198
$559$	0.741575	0.0313653
$560$	−14.2709	−0.603057
$561$	−37.1207	−1.56724
$562$	27.3541	1.15386
$563$	4.42227	0.186377	0.0931883	−	0.995649i	$-0.470294\pi$
$563$	4.42227	0.186377	0.0931883	+	0.995649i	$0.470294\pi$
$564$	−1.22217	−0.0514628
$565$	50.7709	2.13595
$566$	5.61152	0.235870
$567$	−42.4402	−1.78232
$568$	−6.78965	−0.284887
$569$	−2.74907	−0.115247	−0.0576234	−	0.998338i	$-0.518352\pi$
$569$	−2.74907	−0.115247	−0.0576234	+	0.998338i	$0.518352\pi$
$570$	33.2290	1.39181
$571$	0.397036	0.0166154	0.00830772	−	0.999965i	$-0.497356\pi$
$571$	0.397036	0.0166154	0.00830772	+	0.999965i	$0.497356\pi$
$572$	0.892651	0.0373236
$573$	29.8737	1.24799
$574$	6.91904	0.288795
$575$	−51.5189	−2.14849
$576$	1.79034	0.0745974
$577$	−26.1168	−1.08726	−0.543629	−	0.839326i	$-0.682950\pi$
$577$	−26.1168	−1.08726	−0.543629	+	0.839326i	$0.682950\pi$
$578$	−2.57631	−0.107160
$579$	−37.4051	−1.55450
$580$	29.1111	1.20877
$581$	7.85583	0.325915
$582$	17.9339	0.743384
$583$	27.7704	1.15013
$584$	−1.97552	−0.0817476
$585$	1.34364	0.0555527
$586$	−12.7314	−0.525928
$587$	−16.3923	−0.676585	−0.338292	−	0.941041i	$-0.609849\pi$
$587$	−16.3923	−0.676585	−0.338292	+	0.941041i	$0.609849\pi$
$588$	16.2995	0.672182
$589$	16.2831	0.670935
$590$	23.6075	0.971903
$591$	−25.2052	−1.03680
$592$	5.28226	0.217100
$593$	37.5763	1.54308	0.771538	−	0.636184i	$-0.219488\pi$
$593$	37.5763	1.54308	0.771538	+	0.636184i	$0.219488\pi$
$594$	11.8234	0.485119
$595$	−54.1989	−2.22194
$596$	−17.2366	−0.706041
$597$	5.32660	0.218003
$598$	1.13205	0.0462928
$599$	2.46953	0.100902	0.0504512	−	0.998727i	$-0.483934\pi$
$599$	2.46953	0.100902	0.0504512	+	0.998727i	$0.483934\pi$
$600$	19.9101	0.812825
$601$	7.75793	0.316453	0.158226	−	0.987403i	$-0.449422\pi$
$601$	7.75793	0.316453	0.158226	+	0.987403i	$0.449422\pi$
$602$	−14.1013	−0.574726
$603$	−7.00696	−0.285346
$604$	−6.84874	−0.278671
$605$	−33.5768	−1.36509
$606$	−5.70331	−0.231681
$607$	−40.3559	−1.63799	−0.818997	−	0.573797i	$-0.805470\pi$
$607$	−40.3559	−1.63799	−0.818997	+	0.573797i	$0.805470\pi$
$608$	−4.04365	−0.163992
$609$	−64.5019	−2.61375
$610$	−21.7763	−0.881695
$611$	0.111619	0.00451561
$612$	6.79944	0.274851
$613$	24.7663	1.00030	0.500151	−	0.865938i	$-0.333278\pi$
$613$	24.7663	1.00030	0.500151	+	0.865938i	$0.333278\pi$
$614$	20.4276	0.824389
$615$	−14.9588	−0.603199
$616$	−16.9741	−0.683905
$617$	33.6016	1.35275	0.676375	−	0.736558i	$-0.263550\pi$
$617$	33.6016	1.35275	0.676375	+	0.736558i	$0.263550\pi$
$618$	13.8894	0.558716
$619$	32.6593	1.31269	0.656344	−	0.754462i	$-0.272102\pi$
$619$	32.6593	1.31269	0.656344	+	0.754462i	$0.272102\pi$
$620$	15.1191	0.607196
$621$	14.9942	0.601697
$622$	19.2019	0.769926
$623$	−0.0171137	−0.000685647 0
$624$	−0.437493	−0.0175137
$625$	12.2681	0.490723
$626$	−9.44571	−0.377527
$627$	39.5231	1.57840
$628$	1.48927	0.0594284
$629$	20.0613	0.799895
$630$	−25.5498	−1.01793
$631$	−33.9088	−1.34989	−0.674944	−	0.737869i	$-0.735832\pi$
$631$	−33.9088	−1.34989	−0.674944	+	0.737869i	$0.735832\pi$
$632$	−1.26418	−0.0502862
$633$	−9.25791	−0.367969
$634$	21.8744	0.868744
$635$	−57.2941	−2.27365
$636$	−13.6104	−0.539688
$637$	−1.48861	−0.0589807
$638$	34.6252	1.37082
$639$	−12.1558	−0.480875
$640$	−3.75457	−0.148413
$641$	47.9757	1.89492	0.947462	−	0.319867i	$-0.103638\pi$
$641$	47.9757	1.89492	0.947462	+	0.319867i	$0.103638\pi$
$642$	−20.9819	−0.828089
$643$	−44.0577	−1.73747	−0.868734	−	0.495280i	$-0.835066\pi$
$643$	−44.0577	−1.73747	−0.868734	+	0.495280i	$0.835066\pi$
$644$	−21.5263	−0.848253
$645$	30.4867	1.20041
$646$	−15.3572	−0.604221
$647$	26.4164	1.03854	0.519268	−	0.854611i	$-0.326205\pi$
$647$	26.4164	1.03854	0.519268	+	0.854611i	$0.326205\pi$
$648$	−11.1657	−0.438630
$649$	28.0791	1.10220
$650$	−1.81835	−0.0713215
$651$	−33.4995	−1.31295
$652$	−2.76205	−0.108170
$653$	18.9386	0.741125	0.370563	−	0.928807i	$-0.379165\pi$
$653$	18.9386	0.741125	0.370563	+	0.928807i	$0.379165\pi$
$654$	−5.73474	−0.224246
$655$	37.7537	1.47516
$656$	1.82035	0.0710726
$657$	−3.53685	−0.137986
$658$	−2.12247	−0.0827424
$659$	28.5725	1.11303	0.556513	−	0.830839i	$-0.312139\pi$
$659$	28.5725	1.11303	0.556513	+	0.830839i	$0.312139\pi$
$660$	36.6976	1.42845
$661$	34.3770	1.33711	0.668556	−	0.743662i	$-0.266913\pi$
$661$	34.3770	1.33711	0.668556	+	0.743662i	$0.266913\pi$
$662$	1.22429	0.0475835
$663$	−1.66153	−0.0645286
$664$	2.06681	0.0802078
$665$	57.7067	2.23777
$666$	9.45704	0.366453
$667$	43.9111	1.70025
$668$	12.4856	0.483084
$669$	−50.7756	−1.96310
$670$	14.6945	0.567699
$671$	−25.9010	−0.999898
$672$	8.31907	0.320915
$673$	41.3784	1.59502	0.797509	−	0.603307i	$-0.206151\pi$
$673$	41.3784	1.59502	0.797509	+	0.603307i	$0.206151\pi$
$674$	−4.05219	−0.156084
$675$	−24.0845	−0.927011
$676$	−12.9600	−0.498463
$677$	−23.5832	−0.906376	−0.453188	−	0.891415i	$-0.649713\pi$
$677$	−23.5832	−0.906376	−0.453188	+	0.891415i	$0.649713\pi$
$678$	−29.5963	−1.13664
$679$	31.1447	1.19522
$680$	−14.2593	−0.546820
$681$	−28.2164	−1.08125
$682$	17.9828	0.688599
$683$	34.1435	1.30647	0.653233	−	0.757157i	$-0.273412\pi$
$683$	34.1435	1.30647	0.653233	+	0.757157i	$0.273412\pi$
$684$	−7.23951	−0.276810
$685$	5.28775	0.202034
$686$	1.69973	0.0648960
$687$	4.43762	0.169306
$688$	−3.70994	−0.141440
$689$	1.24301	0.0473551
$690$	46.5394	1.77172
$691$	36.8574	1.40212	0.701060	−	0.713102i	$-0.252711\pi$
$691$	36.8574	1.40212	0.701060	+	0.713102i	$0.252711\pi$
$692$	19.8687	0.755295
$693$	−30.3893	−1.15439
$694$	16.0307	0.608517
$695$	−48.8881	−1.85443
$696$	−16.9700	−0.643245
$697$	6.91341	0.261864
$698$	−1.01321	−0.0383507
$699$	3.99271	0.151018
$700$	34.5765	1.30687
$701$	−26.4340	−0.998400	−0.499200	−	0.866487i	$-0.666373\pi$
$701$	−26.4340	−0.998400	−0.499200	+	0.866487i	$0.666373\pi$
$702$	0.529218	0.0199740
$703$	−21.3597	−0.805594
$704$	−4.46575	−0.168309
$705$	4.58874	0.172822
$706$	−24.0513	−0.905182
$707$	−9.90457	−0.372500
$708$	−13.7617	−0.517196
$709$	−12.3466	−0.463686	−0.231843	−	0.972753i	$-0.574476\pi$
$709$	−12.3466	−0.463686	−0.231843	+	0.972753i	$0.574476\pi$
$710$	25.4922	0.956707
$711$	−2.26330	−0.0848805
$712$	−0.00450249	−0.000168738 0
$713$	22.8056	0.854075
$714$	31.5946	1.18240
$715$	−3.35153	−0.125340
$716$	9.27663	0.346684
$717$	9.54987	0.356646
$718$	3.89641	0.145413
$719$	−28.0006	−1.04425	−0.522124	−	0.852870i	$-0.674860\pi$
$719$	−28.0006	−1.04425	−0.522124	+	0.852870i	$0.674860\pi$
$720$	−6.72196	−0.250513
$721$	24.1209	0.898309
$722$	−2.64886	−0.0985803
$723$	−4.72865	−0.175860
$724$	−7.26517	−0.270008
$725$	−70.5322	−2.61950
$726$	19.5732	0.726430
$727$	30.3533	1.12574	0.562872	−	0.826544i	$-0.309697\pi$
$727$	30.3533	1.12574	0.562872	+	0.826544i	$0.309697\pi$
$728$	−0.759765	−0.0281588
$729$	−2.60632	−0.0965305
$730$	7.41724	0.274524
$731$	−14.0898	−0.521131
$732$	12.6942	0.469191
$733$	30.6356	1.13155	0.565776	−	0.824559i	$-0.308577\pi$
$733$	30.6356	1.13155	0.565776	+	0.824559i	$0.308577\pi$
$734$	21.3265	0.787177
$735$	−61.1978	−2.25732
$736$	−5.66339	−0.208755
$737$	17.4779	0.643806
$738$	3.25904	0.119967
$739$	−21.4259	−0.788163	−0.394081	−	0.919076i	$-0.628937\pi$
$739$	−21.4259	−0.788163	−0.394081	+	0.919076i	$0.628937\pi$
$740$	−19.8326	−0.729063
$741$	1.76907	0.0649884
$742$	−23.6363	−0.867717
$743$	−1.45399	−0.0533417	−0.0266708	−	0.999644i	$-0.508491\pi$
$743$	−1.45399	−0.0533417	−0.0266708	+	0.999644i	$0.508491\pi$
$744$	−8.81347	−0.323118
$745$	64.7163	2.37102
$746$	−16.7562	−0.613487
$747$	3.70029	0.135386
$748$	−16.9603	−0.620128
$749$	−36.4379	−1.33141
$750$	−33.6660	−1.22931
$751$	24.5765	0.896810	0.448405	−	0.893830i	$-0.351992\pi$
$751$	24.5765	0.896810	0.448405	+	0.893830i	$0.351992\pi$
$752$	−0.558405	−0.0203630
$753$	−25.8581	−0.942320
$754$	1.54983	0.0564416
$755$	25.7141	0.935832
$756$	−10.0633	−0.365997
$757$	20.9774	0.762435	0.381218	−	0.924485i	$-0.375505\pi$
$757$	20.9774	0.762435	0.381218	+	0.924485i	$0.375505\pi$
$758$	−25.3660	−0.921335
$759$	55.3547	2.00925
$760$	15.1822	0.550716
$761$	−44.6976	−1.62029	−0.810144	−	0.586231i	$-0.800611\pi$
$761$	−44.6976	−1.62029	−0.810144	+	0.586231i	$0.800611\pi$
$762$	33.3989	1.20991
$763$	−9.95916	−0.360546
$764$	13.6492	0.493810
$765$	−25.5290	−0.923003
$766$	23.3647	0.844202
$767$	1.25683	0.0453815
$768$	2.18868	0.0789773
$769$	9.43366	0.340187	0.170093	−	0.985428i	$-0.445593\pi$
$769$	9.43366	0.340187	0.170093	+	0.985428i	$0.445593\pi$
$770$	63.7304	2.29668
$771$	51.8584	1.86763
$772$	−17.0902	−0.615090
$773$	−22.1167	−0.795482	−0.397741	−	0.917498i	$-0.630206\pi$
$773$	−22.1167	−0.795482	−0.397741	+	0.917498i	$0.630206\pi$
$774$	−6.64205	−0.238744
$775$	−36.6314	−1.31584
$776$	8.19392	0.294145
$777$	43.9435	1.57646
$778$	0.275532	0.00987830
$779$	−7.36086	−0.263730
$780$	1.64260	0.0588145
$781$	30.3209	1.08497
$782$	−21.5087	−0.769151
$783$	20.5279	0.733608
$784$	7.44719	0.265971
$785$	−5.59158	−0.199572
$786$	−22.0081	−0.785003
$787$	−1.49668	−0.0533510	−0.0266755	−	0.999644i	$-0.508492\pi$
$787$	−1.49668	−0.0533510	−0.0266755	+	0.999644i	$0.508492\pi$
$788$	−11.5161	−0.410245
$789$	−69.7908	−2.48462
$790$	4.74644	0.168871
$791$	−51.3979	−1.82750
$792$	−7.99520	−0.284097
$793$	−1.15934	−0.0411693
$794$	−20.3216	−0.721188
$795$	51.1013	1.81238
$796$	2.43370	0.0862602
$797$	−1.37411	−0.0486734	−0.0243367	−	0.999704i	$-0.507747\pi$
$797$	−1.37411	−0.0486734	−0.0243367	+	0.999704i	$0.507747\pi$
$798$	−33.6394	−1.19082
$799$	−2.12074	−0.0750265
$800$	9.09682	0.321621
$801$	−0.00806098	−0.000284821 0
$802$	27.2939	0.963782
$803$	8.82218	0.311328
$804$	−8.56599	−0.302099
$805$	80.8219	2.84860
$806$	0.804918	0.0283520
$807$	−34.5969	−1.21787
$808$	−2.60582	−0.0916724
$809$	46.5674	1.63722	0.818612	−	0.574347i	$-0.194744\pi$
$809$	46.5674	1.63722	0.818612	+	0.574347i	$0.194744\pi$
$810$	41.9225	1.47300
$811$	−1.30268	−0.0457432	−0.0228716	−	0.999738i	$-0.507281\pi$
$811$	−1.30268	−0.0457432	−0.0228716	+	0.999738i	$0.507281\pi$
$812$	−29.4706	−1.03422
$813$	67.1696	2.35574
$814$	−23.5893	−0.826803
$815$	10.3703	0.363256
$816$	8.31230	0.290989
$817$	15.0017	0.524844
$818$	−34.2077	−1.19604
$819$	−1.36024	−0.0475305
$820$	−6.83463	−0.238676
$821$	−41.4052	−1.44505	−0.722526	−	0.691344i	$-0.757019\pi$
$821$	−41.4052	−1.44505	−0.722526	+	0.691344i	$0.757019\pi$
$822$	−3.08243	−0.107512
$823$	33.6726	1.17375	0.586877	−	0.809676i	$-0.300357\pi$
$823$	33.6726	1.17375	0.586877	+	0.809676i	$0.300357\pi$
$824$	6.34603	0.221074
$825$	−88.9134	−3.09557
$826$	−23.8990	−0.831553
$827$	19.8837	0.691423	0.345712	−	0.938341i	$-0.387638\pi$
$827$	19.8837	0.691423	0.345712	+	0.938341i	$0.387638\pi$
$828$	−10.1394	−0.352368
$829$	−24.5801	−0.853701	−0.426851	−	0.904322i	$-0.640377\pi$
$829$	−24.5801	−0.853701	−0.426851	+	0.904322i	$0.640377\pi$
$830$	−7.75999	−0.269353
$831$	18.5790	0.644498
$832$	−0.199888	−0.00692988
$833$	28.2833	0.979959
$834$	28.4987	0.986831
$835$	−46.8782	−1.62229
$836$	18.0579	0.624547
$837$	10.6613	0.368509
$838$	−24.3918	−0.842601
$839$	0.148780	0.00513647	0.00256824	−	0.999997i	$-0.499183\pi$
$839$	0.148780	0.00513647	0.00256824	+	0.999997i	$0.499183\pi$
$840$	−31.2346	−1.07769
$841$	31.1167	1.07299
$842$	16.2589	0.560318
$843$	59.8695	2.06202
$844$	−4.22990	−0.145599
$845$	48.6594	1.67394
$846$	−0.999735	−0.0343716
$847$	33.9915	1.16796
$848$	−6.21854	−0.213545
$849$	12.2818	0.421512
$850$	34.5484	1.18500
$851$	−29.9155	−1.02549
$852$	−14.8604	−0.509109
$853$	−8.49829	−0.290976	−0.145488	−	0.989360i	$-0.546475\pi$
$853$	−8.49829	−0.290976	−0.145488	+	0.989360i	$0.546475\pi$
$854$	22.0452	0.754371
$855$	27.1813	0.929580
$856$	−9.58654	−0.327661
$857$	−21.3104	−0.727950	−0.363975	−	0.931409i	$-0.618581\pi$
$857$	−21.3104	−0.727950	−0.363975	+	0.931409i	$0.618581\pi$
$858$	1.95373	0.0666993
$859$	53.6575	1.83077	0.915385	−	0.402579i	$-0.131886\pi$
$859$	53.6575	1.83077	0.915385	+	0.402579i	$0.131886\pi$
$860$	13.9293	0.474984
$861$	15.1436	0.516092
$862$	17.1386	0.583744
$863$	−2.24339	−0.0763658	−0.0381829	−	0.999271i	$-0.512157\pi$
$863$	−2.24339	−0.0763658	−0.0381829	+	0.999271i	$0.512157\pi$
$864$	−2.64757	−0.0900721
$865$	−74.5986	−2.53643
$866$	−15.0689	−0.512061
$867$	−5.63873	−0.191501
$868$	−15.3058	−0.519512
$869$	5.64549	0.191510
$870$	63.7150	2.16014
$871$	0.782316	0.0265078
$872$	−2.62018	−0.0887305
$873$	14.6699	0.496501
$874$	22.9008	0.774631
$875$	−58.4655	−1.97649
$876$	−4.32379	−0.146087
$877$	−8.96344	−0.302674	−0.151337	−	0.988482i	$-0.548358\pi$
$877$	−8.96344	−0.302674	−0.151337	+	0.988482i	$0.548358\pi$
$878$	0.583000	0.0196753
$879$	−27.8650	−0.939862
$880$	16.7670	0.565215
$881$	−38.1543	−1.28545	−0.642726	−	0.766096i	$-0.722197\pi$
$881$	−38.1543	−1.28545	−0.642726	+	0.766096i	$0.722197\pi$
$882$	13.3330	0.448945
$883$	−26.1180	−0.878942	−0.439471	−	0.898257i	$-0.644834\pi$
$883$	−26.1180	−0.878942	−0.439471	+	0.898257i	$0.644834\pi$
$884$	−0.759147	−0.0255329
$885$	51.6693	1.73684
$886$	11.1295	0.373903
$887$	−37.1594	−1.24769	−0.623845	−	0.781548i	$-0.714430\pi$
$887$	−37.1594	−1.24769	−0.623845	+	0.781548i	$0.714430\pi$
$888$	11.5612	0.387969
$889$	58.0017	1.94531
$890$	0.0169049	0.000566655 0
$891$	49.8632	1.67048
$892$	−23.1991	−0.776765
$893$	2.25800	0.0755610
$894$	−37.7256	−1.26173
$895$	−34.8298	−1.16423
$896$	3.80095	0.126981
$897$	2.47769	0.0827278
$898$	20.7888	0.693732
$899$	31.2221	1.04131
$900$	16.2864	0.542880
$901$	−23.6171	−0.786800
$902$	−8.12921	−0.270673
$903$	−30.8633	−1.02707
$904$	−13.5224	−0.449749
$905$	27.2776	0.906739
$906$	−14.9897	−0.498001
$907$	36.4063	1.20885	0.604426	−	0.796662i	$-0.293403\pi$
$907$	36.4063	1.20885	0.604426	+	0.796662i	$0.293403\pi$
$908$	−12.8919	−0.427834
$909$	−4.66530	−0.154738
$910$	2.85259	0.0945626
$911$	−28.4474	−0.942504	−0.471252	−	0.881999i	$-0.656198\pi$
$911$	−28.4474	−0.942504	−0.471252	+	0.881999i	$0.656198\pi$
$912$	−8.85028	−0.293062
$913$	−9.22985	−0.305463
$914$	−25.0136	−0.827378
$915$	−47.6613	−1.57564
$916$	2.02753	0.0669915
$917$	−38.2200	−1.26214
$918$	−10.0551	−0.331867
$919$	23.2964	0.768477	0.384238	−	0.923234i	$-0.374464\pi$
$919$	23.2964	0.768477	0.384238	+	0.923234i	$0.374464\pi$
$920$	21.2636	0.701041
$921$	44.7095	1.47323
$922$	13.7411	0.452538
$923$	1.35717	0.0446719
$924$	−37.1509	−1.22217
$925$	48.0518	1.57993
$926$	−6.18764	−0.203338
$927$	11.3615	0.373162
$928$	−7.75350	−0.254521
$929$	−38.7991	−1.27296	−0.636479	−	0.771294i	$-0.719610\pi$
$929$	−38.7991	−1.27296	−0.636479	+	0.771294i	$0.719610\pi$
$930$	33.0908	1.08509
$931$	−30.1138	−0.986941
$932$	1.82425	0.0597553
$933$	42.0269	1.37590
$934$	21.2399	0.694991
$935$	63.6785	2.08251
$936$	−0.357868	−0.0116973
$937$	28.5038	0.931179	0.465589	−	0.885001i	$-0.345842\pi$
$937$	28.5038	0.931179	0.465589	+	0.885001i	$0.345842\pi$
$938$	−14.8760	−0.485719
$939$	−20.6737	−0.674660
$940$	2.09657	0.0683827
$941$	14.5757	0.475153	0.237576	−	0.971369i	$-0.423647\pi$
$941$	14.5757	0.475153	0.237576	+	0.971369i	$0.423647\pi$
$942$	3.25955	0.106202
$943$	−10.3093	−0.335718
$944$	−6.28765	−0.204646
$945$	37.7832	1.22909
$946$	16.5677	0.538662
$947$	−4.87396	−0.158382	−0.0791912	−	0.996859i	$-0.525234\pi$
$947$	−4.87396	−0.158382	−0.0791912	+	0.996859i	$0.525234\pi$
$948$	−2.76688	−0.0898642
$949$	0.394884	0.0128185
$950$	−36.7844	−1.19344
$951$	47.8762	1.55249
$952$	14.4354	0.467855
$953$	−0.0557414	−0.00180564	−0.000902820	−	1.00000i	$-0.500287\pi$
$953$	−0.0557414	−0.00180564	−0.000902820		1.00000i	$0.500287\pi$
$954$	−11.1333	−0.360454
$955$	−51.2468	−1.65831
$956$	4.36329	0.141119
$957$	75.7836	2.44973
$958$	3.40279	0.109939
$959$	−5.35305	−0.172859
$960$	−8.21758	−0.265221
$961$	−14.7846	−0.476922
$962$	−1.05586	−0.0340424
$963$	−17.1631	−0.553075
$964$	−2.16050	−0.0695850
$965$	64.1664	2.06559
$966$	−47.1142	−1.51587
$967$	19.0496	0.612595	0.306297	−	0.951936i	$-0.400910\pi$
$967$	19.0496	0.612595	0.306297	+	0.951936i	$0.400910\pi$
$968$	8.94291	0.287436
$969$	−33.6121	−1.07978
$970$	−30.7647	−0.987794
$971$	5.42575	0.174121	0.0870603	−	0.996203i	$-0.472253\pi$
$971$	5.42575	0.174121	0.0870603	+	0.996203i	$0.472253\pi$
$972$	−16.4955	−0.529093
$973$	49.4919	1.58664
$974$	−15.7055	−0.503236
$975$	−3.97979	−0.127455
$976$	5.79993	0.185651
$977$	5.96369	0.190795	0.0953976	−	0.995439i	$-0.469588\pi$
$977$	5.96369	0.190795	0.0953976	+	0.995439i	$0.469588\pi$
$978$	−6.04525	−0.193306
$979$	0.0201070	0.000642622 0
$980$	−27.9610	−0.893182
$981$	−4.69101	−0.149772
$982$	23.4224	0.747440
$983$	34.2414	1.09213	0.546065	−	0.837743i	$-0.316125\pi$
$983$	34.2414	1.09213	0.546065	+	0.837743i	$0.316125\pi$
$984$	3.98417	0.127011
$985$	43.2382	1.37768
$986$	−29.4466	−0.937772
$987$	−4.64541	−0.147865
$988$	0.808280	0.0257148
$989$	21.0109	0.668107
$990$	30.0186	0.954053
$991$	14.1594	0.449789	0.224894	−	0.974383i	$-0.427796\pi$
$991$	14.1594	0.449789	0.224894	+	0.974383i	$0.427796\pi$
$992$	−4.02684	−0.127852
$993$	2.67959	0.0850343
$994$	−25.8071	−0.818551
$995$	−9.13750	−0.289678
$996$	4.52359	0.143336
$997$	39.8141	1.26093	0.630463	−	0.776219i	$-0.282865\pi$
$997$	39.8141	1.26093	0.630463	+	0.776219i	$0.282865\pi$
$998$	−33.8288	−1.07083
$999$	−13.9851	−0.442471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.62	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.62	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.18868 q^{3} +1.00000 q^{4} -3.75457 q^{5} +2.18868 q^{6} +3.80095 q^{7} +1.00000 q^{8} +1.79034 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.18868 q^{3} +1.00000 q^{4} -3.75457 q^{5} +2.18868 q^{6} +3.80095 q^{7} +1.00000 q^{8} +1.79034 q^{9} -3.75457 q^{10} -4.46575 q^{11} +2.18868 q^{12} -0.199888 q^{13} +3.80095 q^{14} -8.21758 q^{15} +1.00000 q^{16} +3.79785 q^{17} +1.79034 q^{18} -4.04365 q^{19} -3.75457 q^{20} +8.31907 q^{21} -4.46575 q^{22} -5.66339 q^{23} +2.18868 q^{24} +9.09682 q^{25} -0.199888 q^{26} -2.64757 q^{27} +3.80095 q^{28} -7.75350 q^{29} -8.21758 q^{30} -4.02684 q^{31} +1.00000 q^{32} -9.77411 q^{33} +3.79785 q^{34} -14.2709 q^{35} +1.79034 q^{36} +5.28226 q^{37} -4.04365 q^{38} -0.437493 q^{39} -3.75457 q^{40} +1.82035 q^{41} +8.31907 q^{42} -3.70994 q^{43} -4.46575 q^{44} -6.72196 q^{45} -5.66339 q^{46} -0.558405 q^{47} +2.18868 q^{48} +7.44719 q^{49} +9.09682 q^{50} +8.31230 q^{51} -0.199888 q^{52} -6.21854 q^{53} -2.64757 q^{54} +16.7670 q^{55} +3.80095 q^{56} -8.85028 q^{57} -7.75350 q^{58} -6.28765 q^{59} -8.21758 q^{60} +5.79993 q^{61} -4.02684 q^{62} +6.80498 q^{63} +1.00000 q^{64} +0.750496 q^{65} -9.77411 q^{66} -3.91376 q^{67} +3.79785 q^{68} -12.3954 q^{69} -14.2709 q^{70} -6.78965 q^{71} +1.79034 q^{72} -1.97552 q^{73} +5.28226 q^{74} +19.9101 q^{75} -4.04365 q^{76} -16.9741 q^{77} -0.437493 q^{78} -1.26418 q^{79} -3.75457 q^{80} -11.1657 q^{81} +1.82035 q^{82} +2.06681 q^{83} +8.31907 q^{84} -14.2593 q^{85} -3.70994 q^{86} -16.9700 q^{87} -4.46575 q^{88} -0.00450249 q^{89} -6.72196 q^{90} -0.759765 q^{91} -5.66339 q^{92} -8.81347 q^{93} -0.558405 q^{94} +15.1822 q^{95} +2.18868 q^{96} +8.19392 q^{97} +7.44719 q^{98} -7.99520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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